Question

(2) Consider the following game: P U M D LR 3,1 0,2 1,2 1,1 0,4 3,1 (a) Show that M is a dominated strategy when mixed strategies are used. (b) Using the observation in part (a) above, find the mixed strategy NE for this game.

Answer 1

3p = 1 & 31-p) = 1 19, +29, + 4(1-2-an = 29, +4,+ 1-9-v. % +29, + 4- 49,- 49, = 4+1 3 = 49, +292 NW - 29, +91 if 9,= v ; 3 = 2V +22 9, - - 2v 93 - I-V-3 +2V = V - 5 Mixed strategy nie is ( 13 1 2 3 4

c 31 1 1,2 D 10,4 | 012 11,1 31 - 3 M is dominated when strategies are higher payoff than that from of cher m Assume that now player chooses to play probability U with probability "P" I D with 3p > 1 & 311-p) to.p >,1 P 13 A 3- 30 1 2 > 3p pe 213 . As long as p&[13, 213] I m is dominated by mixer profile of D ول

caluma believes that solum non plage Assume that a player & plays strategy v with probability "9," ; M with probabilit, la now & player believes that column plate chooses """ with probability "p" I such that For now finding values of P. a, a, player, E(U) = E(M) - EOD) for column Playa Elly - EIRS